Isn't "Which things belong to my wife?" also correct in this context?
'belong to' = patřit + dative
"which things are of my wife?" is not accepted.
Isn't it correct english?
Your version is a literal translation of the Czech sentence, but as ion1122 points out, it is not good English. It would never be used in speech or in writing by a native speaker.
No, it is not correct English.
Why moji and not me? It is the genitive case, right? By the way, google uses moje for this
Both are correct.